Perform the indicated operation. Simplify if possible.
\[
\frac{8}{x+7}-\frac{7 x}{x^{2}-49}
\]
$\frac{8}{x+7}-\frac{7 x}{x^{2}-49}=\square($ Simplify your answer.)

Answer

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Answer

Final Answer: $\boxed{\frac{x-56}{x^2-49}}$

Steps

Step 1 ：Find a common denominator for the two fractions, which is $(x+7)(x-7)$

Step 2 ：Rewrite both fractions with the common denominator: $\frac{8}{x+7} \cdot \frac{x-7}{x-7} - \frac{7x}{x^2-49}$

Step 3 ：Simplify the expression: $\frac{8(x-7)}{(x+7)(x-7)} - \frac{7x}{(x+7)(x-7)}$

Step 4 ：Combine the fractions: $\frac{8(x-7) - 7x}{(x+7)(x-7)}$

Step 5 ：Simplify the numerator: $\frac{8x-56 - 7x}{(x+7)(x-7)}$

Step 6 ：Combine like terms: $\frac{x-56}{(x+7)(x-7)}$

Step 7 ：Final Answer: $\boxed{\frac{x-56}{x^2-49}}$